SharePoint Online, as part of Office365, has a default search center for every SharePoint Online environment. This is https://[yourname].sharepoint.com/search
When you create a new (custom) search center you can redirect all search queries to your search center. You can do this via Site actions –> Site Settings –> Search Settings
When you enter the url of your search center all search queries are redirected to this location.
However this url is being reset once in a while back to de default. So from https://[yourname].sharepoint.com/[YourSearchCenter] back to https://[yourname].sharepoint.com/search
Microsoft recognizes this as a bug and even admitted that this is happening in Office365 Preview (which is SharePoint 2013 Beta). Currently they are working on fixing this.
I was thinking I maybe has something to do when a full crawl is executed or when the user profiles are compilated. Since it’s not possible to check ourselves we just have to wait until Microsoft fixes it. That is one of the (dis)advantages of the cloud. Somebody else will fix it for you, but you cannot fix it yourself.
Microsoft said the only workaround right now is to use the default search center and apply the custom branding to that site.
Rik Dekker 